Pith Number

pith:3TDKEBXL

pith:2018:3TDKEBXLEF2MS2OZL7KTNHP7AQ

not attested not anchored not stored refs pending

On the spectrum of the hierarchical Schr\"{o}dinger operator

Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov

arxiv:1811.05210 v1 · 2018-11-13 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3TDKEBXLEF2MS2OZL7KTNHP7AQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:00:46.605391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcc6a206eb2174c969d95fd5369dff043f1c316f7b9548ae0dd515aa90f43c54

Aliases

arxiv: 1811.05210 · arxiv_version: 1811.05210v1 · doi: 10.48550/arxiv.1811.05210 · pith_short_12: 3TDKEBXLEF2M · pith_short_16: 3TDKEBXLEF2MS2OZ · pith_short_8: 3TDKEBXL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3TDKEBXLEF2MS2OZL7KTNHP7AQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: dcc6a206eb2174c969d95fd5369dff043f1c316f7b9548ae0dd515aa90f43c54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acb45a577a21fc426b6845608176e023fd598b38d26f7717e963985cf70a9c0d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-11-13T11:00:46Z",
    "title_canon_sha256": "a8e1f2ad5265f43ac7c05516906b49030404b444b73ddb9a08545e65a25871c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.05210",
    "kind": "arxiv",
    "version": 1
  }
}